Microeconomics for Business

Uses of microeconomics:

1. Price determination – It explains how the prices of goods and services are determined by the forces of demand and supply in individual markets.
2. Consumer behaviour analysis – It helps in understanding how a consumer allocates limited income among different goods to maximise satisfaction.
3. Business decision-making – It guides firms in deciding what to produce, how much to produce, and how to fix prices so as to maximise profit.
4. Resource allocation – It shows how scarce resources are allocated efficiently among different uses, helping to solve the central economic problems.
5. Formulation of economic policies – It assists the government in framing policies relating to taxation, subsidies, and price control.

Types of supply function

A supply function expresses the relationship between the quantity supplied of a commodity and its determinants. On the basis of the number of variables considered, it is of two types:

1. Individual supply function — shows the quantity supplied by a single producer as a function of price and other factors.
   $Q_{sx} = f(P_x,\ P_r,\ T,\ G,\ \dots)$ where (P_x) = price of the good, (P_r) = prices of related goods, (T) = technology, (G) = goals of the firm.

2. Market supply function — shows the total quantity supplied by all producers in the market, obtained by horizontally summing the individual supply functions.
   $Q_{sx}^{M} = f(P_x,\ P_r,\ T,\ G,\ N,\ \dots)$ where (N) = number of sellers in the market.

On the basis of price alone, the supply function may also be written as linear ((Q_s = a + bP)) or non-linear ((Q_s = a + bP + cP^2)) form.

Law of variable proportions states that as more and more units of a variable factor (labour) are combined with fixed factors (capital, land) in the short run, total product first increases at an increasing rate, then at a diminishing rate, reaches a maximum, and finally declines.

In other words, when the quantity of one input is increased while other inputs remain fixed, the marginal product of the variable input eventually falls.

Causes for raising oligopoly:

1. Large capital investment — Heavy fixed costs of plant and machinery discourage new firms from entering, so only a few large firms survive.
2. Economies of scale — Large firms produce at lower average cost, giving them a cost advantage that small/new firms cannot match.
3. Control over key inputs and patents — A few firms may own or control essential raw materials, technology or patents, blocking entry.
4. Mergers and acquisitions — Existing firms combine to gain market power, reducing the number of sellers.
5. Government policy and licensing — Legal restrictions, licences, patents and franchises limit entry to a few firms.
6. Product differentiation and brand loyalty — Strong brands built through advertising make it hard for new entrants to attract customers.
7. Uncertain market demand — Where demand is uncertain or the market is small, only a few firms find it profitable to operate.

Relationship between elasticity of demand and marginal revenue:

1. MR is positive when demand is elastic (|Ed| > 1), zero when elasticity is unity (|Ed| = 1), and negative when demand is inelastic (|Ed| < 1). A monopolist therefore produces only in the elastic range of the demand curve, where total revenue is still rising.

2. MR and price are linked through elasticity by the formula:

$MR = P\left(1 - \frac{1}{|E_d|}\right)$

So the greater the elasticity of demand, the closer MR is to price (under perfect competition, |Ed| = ∞, hence MR = P); the lower the elasticity, the wider the gap between price and marginal revenue.

Transfer earnings are the minimum amount a factor of production must be paid to keep it in its present use — that is, the payment required to prevent it from moving to its next best alternative employment. It is also called the reserve price or opportunity cost of a factor.

Any payment a factor receives above its transfer earnings is called economic rent. For example, if a worker's next best job pays Rs 20,000 per month, that amount is the worker's transfer earnings; any salary above Rs 20,000 is economic rent.

Economic profit is the difference between total revenue and the sum of both explicit and implicit costs (i.e., the total opportunity cost of all resources used).

$\text{Economic Profit} = \text{Total Revenue} - (\text{Explicit Costs} + \text{Implicit Costs})$

Equivalently,

$\text{Economic Profit} = \text{Accounting Profit} - \text{Implicit Costs}$

where explicit costs are actual payments made (wages, rent, raw materials) and implicit costs are the opportunity costs of self-owned resources (the owner's own labour, capital and land).

Example: If total revenue = Rs 5,00,000, explicit costs = Rs 3,50,000 and implicit costs = Rs 1,00,000, then economic profit = 5,00,000 − (3,50,000 + 1,00,000) = Rs 50,000.

A firm earns only a normal profit when economic profit is zero; a positive value means super-normal profit.

Price discrimination means charging different prices for the same good or service to different buyers or in different markets. Four examples practised in Nepal:

1. Airline tickets — Nepal Airlines and other airlines charge different fares for the same Kathmandu–Pokhara route depending on whether the passenger is a Nepali citizen, a SAARC national, or a foreigner.

2. Cinema halls — QFX and other halls charge lower ticket prices on weekdays/morning shows and higher prices on weekends and public holidays for the same film.

3. Electricity (NEA) — Nepal Electricity Authority charges higher per-unit rates for commercial and industrial consumers than for residential consumers, and also uses block (slab) rates for households.

4. Student and senior-citizen discounts — Museums, national parks (e.g., Chitwan, Sagarmatha), and transport services charge lower entry or fare rates for students, senior citizens, and Nepali nationals compared to other visitors.

Indifference map

An indifference map is a set of two or more indifference curves drawn on the same diagram to represent a consumer's complete scale of preferences. Each curve shows a different level of satisfaction, and curves farther from the origin represent higher satisfaction. Since the curves never intersect and are arranged in order of preference, the map as a whole shows how the consumer ranks all possible combinations of two goods.

The three degrees of returns to scale are:

1. Increasing returns to scale — output increases in a greater proportion than the increase in all inputs (e.g., inputs doubled, output more than doubled).
2. Constant returns to scale — output increases in the same proportion as the increase in all inputs (e.g., inputs doubled, output also doubled).
3. Decreasing returns to scale — output increases in a smaller proportion than the increase in all inputs (e.g., inputs doubled, output less than doubled).

Cost Plus Pricing

Cost plus pricing (also called mark-up pricing or full-cost pricing) is a method of setting the selling price of a product by adding a fixed percentage of profit (mark-up) to the cost of producing or acquiring the product. In other words, the firm first determines the total cost per unit and then adds a predetermined mark-up to arrive at the selling price.

$\text{Selling Price} = \text{Cost per Unit} + \text{Mark-up}$

$\text{Mark-up} = \text{Cost per Unit} \times \text{Mark-up Rate (\%)}$

The "cost" used may be:

• Total cost (fixed cost + variable cost), or
• Variable cost only, or
• Full cost including manufacturing, administrative and selling overheads.

Example: If the cost of producing one unit of a product is Rs 200 and the firm decides a mark-up of 25%, then:

$\text{Selling Price} = 200 + (200 \times 25\%) = 200 + 50 = \text{Rs } 250$

This method is simple, logical and widely used by manufacturers, wholesalers and retailers. Retailers, for instance, buy goods at a certain cost and add a standard mark-up (say 20%) to fix the selling price.

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Uses (Importance) of Cost Plus Pricing

1. Simple and Easy to Use It is the simplest method of price determination. Only the cost figures and a desired mark-up rate are needed. It does not require complex market research or demand estimation, so even small firms can apply it easily.

2. Ensures Recovery of Cost and Profit Since the price is fixed above the cost, the firm is assured of recovering its total cost and earning a reasonable profit. This reduces the risk of selling below cost and suffering losses.

3. Price Stability When firms in an industry use a similar mark-up over cost, prices tend to remain stable. This avoids harmful price wars and creates a healthy competitive environment.

4. Useful for New Products For a newly introduced product, the demand and competitor prices are unknown. Cost plus pricing provides a safe and logical basis for fixing the initial price.

5. Basis for Government Contracts and Public Utilities Government contracts, defence purchases and public utility pricing (electricity, water, transport) are often based on cost plus a fair return, because cost can be verified and profit is kept reasonable.

6. Helps in Competitive Bidding In tender and contract business, firms estimate their cost and add a normal mark-up to quote a price. It provides a rational starting point for bidding.

7. Justifiable to Customers and Society Customers and the public generally accept a price that is based on cost plus a fair profit. It appears fair and non-exploitative, which improves the firm's goodwill.

8. Convenient for Multi-Product Firms A firm producing many products can apply the same mark-up rate to all products, saving time and effort in pricing decisions.

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Conclusion: Cost plus pricing is a cost-oriented method that guarantees cost recovery and a fair profit, and is useful for new products, government contracts, tenders and price stability. However, it ignores demand, competition and consumer willingness to pay, so it should be used along with market-oriented methods for better results.

Scope of Business Economics

Business economics (also called managerial economics) is the application of economic theory and analytical tools to business decision-making. Its scope refers to the areas of economic study that a business manager uses to solve practical problems of the firm. The scope is wide and is generally described under the following heads:

1. Demand Analysis and Forecasting This covers the study of consumer behaviour, the law of demand, elasticity of demand, and the factors affecting demand. The manager must estimate how much of the product will be demanded at different prices. Demand forecasting helps the firm decide production volume, inventory, pricing, and sales promotion. This is one of the most important areas because all production planning depends on correct demand estimates.

2. Production and Cost Analysis This deals with the production function, laws of returns (law of variable proportions and returns to scale), choice of the optimum combination of inputs, and the law of supply. On the cost side, it studies cost concepts — fixed and variable cost, average and marginal cost, short-run and long-run cost curves, and economies of scale. The aim is to produce the desired output at the minimum possible cost.

3. Pricing Decisions and Policies Pricing is central to business economics. It studies price determination under different market structures — perfect competition, monopoly, monopolistic competition, and oligopoly. It also covers pricing methods such as cost-plus pricing, marginal cost pricing, discriminating pricing, and product-line pricing. The objective is to fix a price that maximises profit and captures the market.

4. Profit Analysis and Profit Planning This area examines the meaning and theories of profit, break-even analysis, contribution margin, margin of safety, and the factors that influence profit. Break-even analysis is widely used to determine the output level at which total revenue equals total cost. Profit planning helps the firm set targets and control operations.

5. Capital Budgeting and Investment Decisions This includes the study of capital, capital formation, and the appraisal of investment projects using techniques such as payback period, net present value (NPV), internal rate of return (IRR), and profitability index. It helps the manager decide where and how much to invest in plant, machinery, and expansion.

6. Resource Allocation and Production Planning Business economics studies how scarce resources are allocated among competing uses within the firm. It covers linear programming, input-output analysis, and decision-making under risk and uncertainty. This helps in optimum utilisation of limited resources.

7. Market Structure and Competitive Strategy The manager must understand the nature of competition — number of sellers, nature of the product, entry conditions, and price-output behaviour of rivals. This guides decisions on product differentiation, advertising, and strategic pricing.

8. Government Regulation and Business Environment Business decisions are affected by government policies — taxation, subsidies, price control, monetary and fiscal policy, and industrial policy. The scope therefore includes the study of the economic environment in which the firm operates.

9. Macroeconomic Analysis for Business National income, inflation, business cycles, and balance of payments affect the general level of demand and cost. The manager must study these to anticipate changes in the business climate.

10. Profit Maximisation and Social Responsibility Business economics deals with the objective of the firm — whether to maximise profit, sales revenue, or growth — and also with social obligations such as consumer welfare, employment, and environmental protection.

Conclusion Thus, the scope of business economics extends from demand and cost analysis to pricing, profit planning, investment, resource allocation, and the study of the business environment. It is both microeconomic (firm-level) and macroeconomic in nature, and it uses both theory and quantitative tools to help managers take rational decisions.

Loanable Funds Theory of Interest

The loanable funds theory (also called the neoclassical or credit theory) was developed by Wicksell and refined by Robertson, Ohlin and Haberler. It explains the rate of interest as the price that equates the demand for and supply of loanable funds in the credit market. Unlike the classical theory (interest as reward for saving alone) and Keynes's liquidity preference theory (interest as reward for parting with liquidity), it combines real and monetary factors.

1. Demand for loanable funds ($D_L$)

• Investment demand by firms: the largest component, inversely related to the interest rate. At lower rates more projects are profitable.
• Government borrowing: to finance deficits and public investment, largely interest-inelastic.
• Consumer borrowing: for housing and durables, also inversely related to the rate.
• Demand for hoarding: funds people wish to hold as idle cash balances, which withdraws funds from the market.

The $D_L$ curve slopes downward.

2. Supply of loanable funds ($S_L$)

• Household savings: directly related to the interest rate.
• Business savings: retained earnings of firms.
• Bank credit: new credit created by commercial banks.
• Dishoarding: idle balances brought back to the market.
• Foreign lending: capital inflows.

The $S_L$ curve slopes upward.

3. Determination of the interest rate

$D_L=S_L$

The equilibrium rate $i^*$ is where the curves meet. Above $i^*$, supply exceeds demand and the rate falls. Below $i^*$, demand exceeds supply and the rate rises.

4. Diagram

Take loanable funds on the X-axis and the rate of interest on the Y-axis. $D_L$ falls from left to right and $S_L$ rises from left to right. They intersect at $E$, giving the equilibrium rate $i^*$ and quantity $Q^*$.

5. Shifts

6. Criticisms

1. Indeterminate supply curve: saving depends on income, which depends on investment and so on the interest rate.
2. Full-employment assumption: it ignores unemployment.
3. Ignores liquidity preference: Keynes's criticism.
4. Static analysis: it explains dynamic change poorly.
5. Bank credit is not fully elastic, as some versions assume.

7. Conclusion

The theory improves on the classical view by joining real factors (saving and investment) with monetary factors (bank credit, hoarding and dishoarding). Despite its criticisms, it remains a useful account of how interest rates are set in the credit market.

Law of Diminishing Marginal Rate of Technical Substitution

Meaning

The marginal rate of technical substitution (MRTS) is the rate at which one input can be reduced when one more unit of another input is added, keeping output constant. The law of diminishing MRTS states that as more and more units of one input (say labour) are substituted for another input (say capital), the amount of capital that can be given up for each additional unit of labour goes on falling. In other words, MRTS diminishes along an isoquant as we move from left to right.

Explanation with Schedule

Let output be fixed at 100 units. The combinations of labour (L) and capital (K) on the same isoquant are:

As labour rises from 1 to 2 units, 4 units of capital can be released while output stays at 100. For the next unit of labour only 3 units of capital can be released, then 2, and finally only 1. So MRTS falls from 4 to 3 to 2 to 1 — it diminishes.

Diagram

Plotting these points gives a convex-to-the-origin isoquant. The slope of the isoquant at any point equals the MRTS. Since the slope becomes flatter as we move rightward, the isoquant is convex to the origin — this convexity is the geometric expression of the law.

Reasons

1. Imperfect substitutability of inputs. Labour and capital are not perfect substitutes. Each input is better suited to certain tasks, so substitution becomes progressively harder.
2. Specialisation and factor proportions. When a large amount of capital is already replaced by labour, the remaining capital is more specialised and essential, so less of it can be spared for each extra worker.

Assumptions

1. The production function is continuous and inputs are divisible.
2. The technique of production remains unchanged.
3. Inputs are imperfect substitutes.
4. Output is held constant along the isoquant.

Importance

1. It explains the convex shape of isoquants.
2. It helps determine the least-cost combination of inputs, where MRTS equals the input price ratio (w/r).
3. It guides the producer in choosing the optimum factor combination for a given output.

Conclusion

The law of diminishing MRTS is a fundamental property of isoquants. It shows that substitution between inputs is possible but not unlimited, and it underlies the producer's equilibrium condition MRTS_LK = w/r.

Given: [ Q_d=3000-50P,\qquad Q_s=-1500+50P ]

a. Equilibrium price and quantity

At equilibrium, [ Q_d=Q_s ] [ 3000-50P=-1500+50P ] [ 3000+1500=50P+50P ] [ 4500=100P ] [ P=\frac{4500}{100}=45 ]

So equilibrium price is Rs 45.

Putting (P=45) in demand function: [ Q_d=3000-50(45)=3000-2250=750 ]

Hence equilibrium quantity is 750 units.

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Price elasticity of demand at equilibrium

[ E_d=\frac{dQ_d}{dP}\times \frac{P}{Q_d} ]

Given, [ \frac{dQ_d}{dP}=-50,\quad P=45,\quad Q_d=750 ]

[ E_d=-50\times \frac{45}{750} ] [ E_d=-\frac{2250}{750}=-3 ]

Thus, [ |E_d|=3 ]

Interpretation: Demand is elastic at equilibrium because (|E_d|>1).

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b. Consumer’s surplus, producer’s surplus and total surplus

Consumer’s surplus (CS):

Demand intercept when (Q_d=0): [ 0=3000-50P \Rightarrow P=60 ]

[ CS=\frac12(\text{Demand intercept}-\text{Equilibrium price})\times Q ] [ CS=\frac12(60-45)\times 750 ] [ CS=\frac12\times 15\times 750=5625 ]

So, [ \boxed{CS=\text{Rs }5625} ]

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Producer’s surplus (PS):

Supply intercept when (Q_s=0): [ 0=-1500+50P \Rightarrow P=30 ]

[ PS=\frac12(\text{Equilibrium price}-\text{Supply intercept})\times Q ] [ PS=\frac12(45-30)\times 750 ] [ PS=\frac12\times 15\times 750=5625 ]

So, [ \boxed{PS=\text{Rs }5625} ]

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Total surplus (TS): [ TS=CS+PS ] [ TS=5625+5625=11250 ]

[ \boxed{TS=\text{Rs }11250} ]

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Final Answer:

[ \boxed{P=45,\quad Q=750,\quad E_d=-3} ]

[ \boxed{CS=\text{Rs }5625,\quad PS=\text{Rs }5625,\quad TS=\text{Rs }11250} ]

a. Computation of TFC and TVC

At (Q=0), total cost is Rs 100. Since no variable input is used at zero output, this entire amount is fixed cost.

[ TFC = Rs,100 \quad \text{(constant at all output levels)} ]

[ TVC = TC - TFC ]

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b. Graph and explanation of behaviour

Graph description:

• On the X-axis, take quantity (Q) from 0 to 9.
• On the Y-axis, take cost in Rs.
• Plot the following points and join them smoothly:

TFC curve:
[ (0,100), (1,100), (2,100), \ldots, (9,100) ] It is a horizontal straight line parallel to the X-axis.

TVC curve:
[ (0,0), (1,10), (2,18), (3,24), (4,32), (5,50), (6,80), (7,124), (8,180), (9,260) ] It starts from the origin and rises continuously. It is S-shaped: initially it rises at a decreasing rate, then at an increasing rate.

TC curve:
[ (0,100), (1,110), (2,118), (3,124), (4,132), (5,150), (6,180), (7,224), (8,280), (9,360) ] It starts from Rs 100 on the Y-axis and rises continuously. It has the same shape as the TVC curve but lies above it by the constant amount of TFC.

Behaviour:

1. TFC:
   Total fixed cost remains constant at Rs 100 at every level of output. It does not change with output because fixed factors such as rent, insurance, and salaries of permanent staff must be paid even when production is zero. Hence its graph is a horizontal straight line.

2. TVC:
   Total variable cost is zero at zero output and increases as output increases. Its slope is marginal cost.

   • Up to (Q=3), TVC rises at a decreasing rate because marginal cost falls:
     [ MC = 10, 8, 6 ] This happens due to better utilization of fixed factors and specialization.
   • After (Q=3), TVC rises at an increasing rate because marginal cost rises:
     [ MC = 8, 18, 30, 44, 56, 80 ] This is due to the operation of the law of diminishing returns.
     Thus TVC is S-shaped, with an inflection point at (Q=3), where MC is minimum.

3. TC:
   Total cost is the sum of TFC and TVC: [ TC = TFC + TVC ] At (Q=0), (TC = TFC = Rs,100). As output increases, TC increases continuously. Initially it rises at a decreasing rate up to (Q=3), then at an increasing rate after (Q=3). The TC curve is simply the TVC curve shifted upward by Rs 100. Therefore, TC and TVC have the same slope at every output level, and the vertical distance between them is always equal to TFC.

Meaning of Perfect Competition

Perfect competition is a market structure in which a very large number of buyers and sellers deal in a homogeneous (identical) product at a single price, with complete freedom of entry and exit of firms and perfect knowledge of the market. Because each firm sells only a negligible part of total market supply, no single firm can influence the price — it is a price taker, and the price is set by the industry as a whole through demand and supply.

Its main features are: (i) large number of buyers and sellers, (ii) homogeneous product, (iii) free entry and exit of firms, (iv) perfect knowledge of market conditions, (v) perfect mobility of factors of production, (vi) no transport cost and no selling cost, and (vii) a single uniform price. As a result, for the individual firm,

$AR = MR = P \quad \text{(demand curve is a horizontal straight line)}$

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Price Determination under Perfect Competition (8 marks)

Price under perfect competition is determined by the interaction of market (industry) demand and market supply. The industry is the group of all firms producing the same product, and the industry's demand and supply curves are obtained by horizontal summation of all individual demand and supply curves.

Market demand slopes downward: at a lower price, more is demanded. Market supply slopes upward: at a higher price, firms are willing to supply more. The point at which the two curves intersect is the equilibrium point, and the price corresponding to it is the equilibrium price.

Let $Q_d = f(P)$ and $Q_s = g(P)$. Equilibrium requires:

$Q_d = Q_s$

Why it is stable:

• If the market price rises above equilibrium (say $OP_1$), supply exceeds demand → surplus → sellers compete and cut price → price falls back to $OP$.
• If the price falls below equilibrium (say $OP_2$), demand exceeds supply → shortage → buyers compete and bid up price → price rises back to $OP$.

Thus $OP$ is the only price at which the plans of buyers and sellers match, and it is called the equilibrium price; $OQ$ is the equilibrium quantity.

Numerical illustration: Let $Q_d = 100 - 5P$ and $Q_s = 20 + 5P$. Setting $Q_d = Q_s$:

$100 - 5P = 20 + 5P \;\Rightarrow\; 80 = 10P \;\Rightarrow\; P = 8,\quad Q = 60$

So equilibrium price is Rs 8 and equilibrium quantity 60 units.

Effect of shifts: A rise in demand or a fall in supply raises the equilibrium price; the opposite changes lower it. The equilibrium price determined by the industry becomes the firm's given price, so the firm's average revenue and marginal revenue are both equal to this price.

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Output Determination under Perfect Competition (5 marks)

Once the industry fixes the price, the individual firm is a price taker and must decide how much to produce. It produces that output at which its profit is maximum. This is explained by two approaches.

1. Total Revenue – Total Cost (TR – TC) Approach

$\text{Profit} = TR - TC$

The firm expands output as long as $TR$ rises faster than $TC$ (i.e. $MR > MC$), and stops where further expansion would reduce profit. Profit is maximum at the output where the difference between TR and TC is the greatest, i.e. where the slopes of the TR and TC curves are equal:

$MR = MC$

2. Marginal Revenue – Marginal Cost (MR – MC) Approach

The firm is in equilibrium at the output where:

1. $MR = MC$ (necessary condition), and
2. MC is rising and cuts MR from below (sufficient condition).

If $MR > MC$, an extra unit adds more to revenue than to cost, so profit rises by producing more. If $MR < MC$, an extra unit adds more to cost than to revenue, so profit falls. Hence equilibrium lies exactly where $MR = MC$ with rising MC. Since $MR = P$ under perfect competition, the condition becomes:

$P = MC \quad \text{(with MC rising)}$

Numerical illustration: Suppose $P = \text{Rs }10$ and $TC = 20 + 2Q + 0.5Q^2$. Then $MC = 2 + Q$. Setting $MC = P$: $2 + Q = 10 \Rightarrow Q = 8$ units. Profit $= TR - TC = 80 - (20 + 16 + 32) = \text{Rs }12$. Since MC is rising, 8 units is the profit-maximising output.

Short-run Equilibrium of the Firm

With plant size fixed, the firm may face three situations:

The shut-down point is the minimum point of $AVC$: below this price the firm loses more by producing than by closing down. The firm's short-run supply curve is therefore the portion of $MC$ above minimum $AVC$.

Long-run Equilibrium of the Firm

In the long run all factors are variable and firms can freely enter or leave the industry:

• Supernormal profit attracts new firms → industry supply rises → price falls → profit is competed away.
• Losses drive existing firms out → industry supply falls → price rises → losses disappear.

This process continues until every firm earns only normal profit, at the point where the demand curve (price line) is tangent to the minimum point of the long-run average cost curve:

$P = AR = MR = MC = \text{minimum } LAC$

At this output the firm is of optimum size, resources are allocated efficiently ($P = MC$), and there is no tendency to expand or contract. The industry's long-run equilibrium output is simply the sum of the equilibrium outputs of all its firms at this price.

1. Price effect

The price effect (PE) is the change in the consumer's equilibrium purchases of goods when the price of one good (X) changes, with income, tastes and the price of the other good (Y) unchanged. It is the sum of the substitution effect and the income effect.

$PE = SE + IE$

On an indifference map, joining the equilibrium points obtained as $P_x$ changes gives the price consumption curve (PCC). Its shape depends on how X and Y are related.

2. Price effect for substitutes

Substitutes satisfy the same want (e.g. tea and coffee; Nepal Telecom and Ncell data packs).

When $P_x$ falls, the budget line pivots outward on the X-axis. The consumer buys more X and less Y, because X has become cheaper relative to Y. So the PCC slopes downward (backward): Y falls as X rises.

• The substitution effect is strong, since X easily replaces Y.
• Cross elasticity is positive.
• Demand for X is relatively elastic.

3. Price effect for complements

Complements are used together (e.g. tea and sugar, motorbike and petrol).

When $P_x$ falls, the consumer buys more X and also more Y, because using more X needs more Y. So the PCC slopes upward: Y rises along with X.

• The substitution effect is weak, since X cannot easily replace Y.
• Cross elasticity is negative.
• Demand for X is relatively less elastic.

4. Derivation of the demand curve from the PCC

Let $P_x$ take three values, $P_1>P_2>P_3$.

1. Draw the budget lines for each price, each with the same Y-intercept $M/P_y$ and a steeper or flatter slope.
2. Mark the tangency with the highest attainable indifference curve for each, giving equilibrium points $E_1, E_2, E_3$ and quantities $X_1<X_2<X_3$. Joining these points gives the PCC.
3. Plot each price against its equilibrium quantity of X on a new graph, with price on the Y-axis and quantity of X on the X-axis. The points $(X_1,P_1),(X_2,P_2),(X_3,P_3)$ joined together form the demand curve for X.

The demand curve slopes downward in both cases.

A change in the price of the related good shifts the demand curve for X, while a change in $P_x$ itself moves along it.

a. Computation of Income Elasticity of Demand

Given demand schedule:

Formula

(i) Proportion method

[ E_y=\frac{%\Delta Q}{%\Delta Y} =\frac{\Delta Q/Q}{\Delta Y/Y} =\frac{\Delta Q}{\Delta Y}\times \frac{Y}{Q} ]

where (Y) and (Q) are the initial income and demand.

(ii) Arc method

[ E_y= \frac{\Delta Q}{\frac{Q_1+Q_2}{2}} \div \frac{\Delta Y}{\frac{Y_1+Y_2}{2}} ]

[ E_y=\frac{\Delta Q}{\Delta Y}\times \frac{Y_1+Y_2}{Q_1+Q_2} ]

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1. Movement from B to C

Initial point B:
[ Y_1=20,000,\quad Q_1=200 ]

Final point C:
[ Y_2=30,000,\quad Q_2=300 ]

[ \Delta Y=30,000-20,000=10,000 ]

[ \Delta Q=300-200=100 ]

(i) Proportion method

[ E_y=\frac{100}{10,000}\times \frac{20,000}{200} ]

[ E_y=0.01\times 100=1 ]

[ \boxed{E_y=1} ]

(ii) Arc method

[ E_y=\frac{100}{10,000}\times \frac{20,000+30,000}{200+300} ]

[ E_y=0.01\times \frac{50,000}{500} ]

[ E_y=0.01\times 100=1 ]

[ \boxed{E_y=1} ]

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2. Movement from D to B

Initial point D:
[ Y_1=40,000,\quad Q_1=400 ]

Final point B:
[ Y_2=20,000,\quad Q_2=200 ]

[ \Delta Y=20,000-40,000=-20,000 ]

[ \Delta Q=200-400=-200 ]

(i) Proportion method

[ E_y=\frac{-200}{-20,000}\times \frac{40,000}{400} ]

[ E_y=0.01\times 100=1 ]

[ \boxed{E_y=1} ]

(ii) Arc method

[ E_y=\frac{-200}{-20,000}\times \frac{40,000+20,000}{400+200} ]

[ E_y=0.01\times \frac{60,000}{600} ]

[ E_y=0.01\times 100=1 ]

[ \boxed{E_y=1} ]

Conclusion

In both movements, income elasticity of demand is:

[ \boxed{E_y=1} ]

This means demand changes in the same proportion as income. Such a good is a normal good with unitary income elasticity.

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b. Difference between Price Elasticity of Demand and Cross Elasticity of Demand

Thus, price elasticity studies the effect of a good’s own price, while cross elasticity studies the effect of the price of a related good.